How Can I Calculate the Angle Between a Line and the Horizontal Axis?

Calculate the angle between the straight line and the horizontal axis

In programming, it is often necessary to determine the angle between a straight line and the horizontal axis. Consider the following diagram, where (P1_x,P1_y) and (P2_x,P2_y) define in the positive quadrant A directed line segment. Our goal is to find the angle θ between this line and the horizontal axis.

Steps to calculate the included angle:

1. Calculate vector components: Find the difference between endpoints:

• deltaY = P2_y - P1_y
• deltaX = P2_x - P1_x

2. Use arctan2 to calculate the angle (recommended):

• angleInDegrees = atan2(deltaY, deltaX) * 180 / PI

This method uses the atan2 function, which considers deltaY and deltaX to determine the correct angles in all quadrants.

3. Alternative method:

• Treat vector (deltaX, deltaY) as a unit vector by dividing it by its length.
• deltaX becomes the cosine of the angle, and deltaY becomes the sine of the angle.
• If the vector length is 0, there is no angle, so sine and cosine are undefined.

Other notes:

• The sign of deltaX and deltaY determines the quadrant of the angle.
• atan2(deltaY, deltaX) returns the angle in radians. Multiply by 180 / PI to convert it to degrees.

Python example implementation:

<code class="language-python">from math import atan2, pi

def get_angle_between_points(x1, y1, x2, y2):
    deltaY = y2 - y1
    deltaX = x2 - x1
    angle_in_radians = atan2(deltaY, deltaX)
    angle_in_degrees = angle_in_radians * 180 / pi
    return angle_in_degrees</code>

This function accepts four coordinates and returns the angle in degrees.

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